Permeation as Exponential Processes

It has been tacitly assumed that permeation and, more generally, diffusion into closed volumes like living cells lead to an increase in concentration of the permeant within the cell which follows an exponential time curve. On this basis permeation may be treated mathematically as a unimolecular reaction. Since permeation reaches an equilibrium when the external (Cg) and internal (Cf) concentrations are equal, this equivalent unimolecular reaction must be reversible, with K = fci/fe = 1. This of course neglects changes in activity coefficients of the permeant. 

fundamental equations of Fick (22) describe the rate of unidimensional diffusion of material moving along an infinite system. It is important to examine the validity of the assumption that these equations describe to a satisfactory degree the situation in quite different systems. For example, the experimental evidence available in biology concerns permeation into spherical cells or cylinders, or cells with more complicated shapes, like the frequently observed mammalian erythroc3rtes. 

The Fick equations deal with the statistical result of movement of large numbers of molecules, and these are satisfactory for the present purpose. The equation is  

Here dn is the amount of substance which passes across an area, a, in an ideal plane transverse to the diffusion in time, dt, where the concentration gradient is dc/dx. D is the diffusion constant of the reactant. For use, the latter equation, often termed the fundamental equation, must be integrated. Stefan s (81) solution modified by Svedberg (83) applies to diffusion of a solute in a vessel of uniform cross section from an infinitely long column of solution into a similar column of solute. This treatment follows that 

Is this dependence valid for other systems In the first place, permeation into cells is ordinarily considered to take place from a relatively large volume of well-stirred medium, so that Co remains essentially constant. Therefore the co/2 of the equation above becomes co. Any deviation from these conditions merits special treatment. 

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